One of the most crucial concepts to master about FRW models is the
existence of horizons. This concept will prove useful in a
variety of places in these lectures, but most importantly in
understanding the shortcomings of what we are terming the standard
cosmology.

Suppose an emitter, e, sends a light signal to an observer,
o, who is at r = 0. Setting
= constant and
= constant and
working in conformal time, for such radial null rays we have
o -
= r. In particular
this means that

(46)

Now suppose e is
bounded below by
e; for
example,
e might
represent the Big Bang singularity.
Then there exists a maximum distance to which the observer can see,
known as the particle horizon distance, given by

Figure 2.3. Particle horizons arise when the
past light cone of an observer o terminates at a finite
conformal time. Then there will be worldlines of other particles which
do not intersect the past of o, meaning that they were never in
causal contact.

Similarly, suppose o
is bounded above by
o. Then
there exists a limit to spacetime events which can be influenced by the
emitter. This limit is known as the event horizon distance, given
by

Figure 2.4. Event horizons arise when the
future light cone of an observer o terminates at a finite
conformal time. Then there will be worldlines of other particles which
do not intersect the future of o, meaning that
they cannot possibly influence each other.

These horizon distances may be converted to proper horizon
distances at cosmic time t, for example

(49)

Just as the Hubble time H0-1 provides a
rough guide for the age of the universe, the Hubble distance
cH0-1 provides a rough estimate of the
horizon distance in a matter- or radiation-dominated universe.